Write an equation in standard form for the line that passes through the given points (0,-3) and (7,0)

The equation in standard form that passes through (0, -3) and (7, 0) is 3x – 7y = 21Solution:Given, two points are (0, -3) and (7, 0) We have to find that a line that passes through the given two points in standard form. First let us find the slope of the line that passes through given two points. The slope of the line "m" is given as:[tex]\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }[/tex][tex]\text { So slope of our line }=\frac{-3-0}{0-7}=\frac{-3}{-7}=\frac{3}{7}[/tex]Now, let us find the line equation using point slope form:[tex]\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { is point on the line. }[/tex][tex]\text { Then, line equation } \rightarrow y-0=\frac{3}{7}(x-7)[/tex]7(y – 0) = 3(x – 7) 7y = 3x – 21 3x – 7y = 21 Hence, the line equation in standard form is 3x – 7y = 21.